How to Find GCF of 87/78, 123/16, 499/564?

GCF of 87/78, 123/16, 499/564

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 87/78, 123/16, 499/564 i.e 1/29328 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/78, 123/16, 499/564.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 87/78,123/16,499/564?

Given fractions are 87/78,123/16,499/564

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 87/78,123/16,499/564, numerators are 87,123,499

Denominators are 78,16,564

The GCF of 87,123,499 is 1 .

LCM of 78,16,564 is 29328.

The greatest common factor of 87/78,123/16,499/564 = [GCF of 87,123,499]/[LCM of 78,16,564]= 1/29328

Therefore, the GCF of 87/78,123/16,499/564 is 1/29328.

Greatest Common Factor of 87,123,499

To find the highest common factor of 87,123,499, we have to find the factors of both numbers and list the highest common factor.

The factors of 87 are 1, 3, 29, 87

The factors of 123 are 1, 3, 41, 123

The factors of 499 are 1, 499

The HCF of 87,123,499 is 1.

Lets's calculate GCF of 87,123,499

Greatest Common Factor (GCF) of 87,123,499 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 87,123,499 By Matching Biggest Common Factor Method

Now, list down the factors of 87

1,3,29,87

Now, list down the factors of 123

1,3,41,123

Now, list down the factors of 499

1,499

Greatest Common Factor

We found the factors 87,123,499 . The biggest common factor number is the GCF number.
So the greatest common factor 87,123,499 is 1.

Lets's calculate LCM of 78,16,564

Lowest Common Multiple of 78,16,564 using Common Division

2	78, 16, 564
2	39, 8, 282
3	39, 4, 141
	13, 4, 47

∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 4 x 47 = 29328

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29328

Therefore, the GCF of Fractions 87/78,123/16,499/564 is 1/29328

Least Common Multiple of 78,16,564 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 78,16,564 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,16,564) = 2

common factors(in case of two or more numbers have common factors) = 12

GCF(78,16,564) x common factors =2 x 12 = 24

LCM(78,16,564) = ( 78 × 16 × 564 ) / 24

LCM(78,16,564) = 703872 / 24

LCM(78,16,564) = 29328

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FAQs on GCF of Fractions of 87/78, 123/16, 499/564

1. What is the HCF of 87,123,499?

The HCF of 87,123,499 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 87/78, 123/16, 499/564?

Answer: GCF of Numerators as per given numbers 87/78, 123/16, 499/564 is

GCF of Numerators i.e. for 87,123,499 is 1

LCM of denominators i.e. for 78,16,564 is 29328.

Thus, GCF of Fractions is 1/29328.Finally, GCF of Fractions for 87/78, 123/16, 499/564 is 1/29328.